Class 7 Maths All Formulas: The Complete CBSE Formula Sheet (2026)

Addition rules:
- Same sign: Add the absolute values, keep the sign.
- Different signs: Subtract the smaller absolute value from the larger, keep the sign of the larger.

Multiplication and division rules:

Same rules apply for division.

Properties of integers:
- Closure: Integers are closed under addition, subtraction, and multiplication.
- Commutative: $a + b = b + a$ and $a \times b = b \times a$
- Associative: $(a + b) + c = a + (b + c)$
- Distributive: $a \times (b + c) = a \times b + a \times c$
- Additive identity: $a + 0 = a$
- Multiplicative identity: $a \times 1 = a$

Memory tip: For multiplication: same signs give positive, different signs give negative. Think of it as "friends of friends are friends (+), enemies of enemies are friends (+), friends of enemies are enemies (-)."

Multiplication of fractions:

Division of fractions (multiply by the reciprocal):

Reciprocal: The reciprocal of $\frac{a}{b}$ is $\frac{b}{a}$.

Multiplication of mixed fractions: Convert to improper fractions first, then multiply.

Decimal operations:
- Multiplication of decimals: Multiply as whole numbers, then count total decimal places.

• Division of a decimal by a whole number: Divide normally, place the decimal point directly above.
  
  $$4.8 \div 2 = 2.4$$
• Division of a decimal by a decimal: Make the divisor a whole number by multiplying both by $10$ or $100$.
  
  $$3.6 \div 0.4 = 36 \div 4 = 9$$

Memory tip: To divide fractions, flip the second fraction and multiply. "Dividing by a fraction is multiplying by its reciprocal."

A simple equation is a statement of equality involving a variable.

General form: $ax + b = c$ where $x$ is the variable.

Solution method (transposing):
Move terms to the opposite side by changing their sign.

Example: Solve $3x + 5 = 17$.

Verification: Substitute back: $3(4) + 5 = 12 + 5 = 17$. Correct.

Key principle: Whatever operation you perform on one side, you must perform on the other side too. Adding, subtracting, multiplying, or dividing the same number on both sides keeps the equation balanced.

Memory tip: Transposing means moving a term to the other side with its sign flipped: $+$ becomes $-$, $\times$ becomes $\div$.

Complementary angles: Two angles whose sum is $90°$.

Supplementary angles: Two angles whose sum is $180°$.

Adjacent angles: Angles that share a common vertex and a common arm.

Linear pair: Adjacent angles that form a straight line. They are always supplementary.

Vertically opposite angles: When two lines intersect, the angles opposite each other are equal.

Angles made by a transversal with parallel lines:
- Corresponding angles are equal
- Alternate interior angles are equal
- Co-interior angles (same-side interior) sum to $180°$

Memory tip: Complementary = Corner ($90°$, like a right-angle corner). Supplementary = Straight ($180°$, like a straight line).

Angle sum property:

Exterior angle property: An exterior angle of a triangle equals the sum of the two non-adjacent interior angles.

Triangle inequality:
The sum of any two sides must be greater than the third side.

Difference inequality:
The difference of any two sides must be less than the third side.

Pythagoras theorem (for right-angled triangles):

Common Pythagorean triplets: $(3, 4, 5)$, $(5, 12, 13)$, $(8, 15, 17)$, $(7, 24, 25)$.

Types of triangles:
- By sides: Equilateral (all equal), Isosceles (two equal), Scalene (none equal)
- By angles: Acute (all $< 90°$), Right (one $= 90°$), Obtuse (one $> 90°$)

Memory tip: The angle sum is $180°$, always. If you know two angles, the third is $180°$ minus the other two.

Ratio: A comparison of two quantities of the same kind.

Proportion: An equality of two ratios.

Percentage:

Converting between fractions, decimals, and percentages:

• Fraction to percentage: multiply by $100$
  - Percentage to fraction: divide by $100$
  - Decimal to percentage: multiply by $100$

Profit and Loss:

Simple Interest:

Memory tip: Profit and loss percentages are always calculated on the Cost Price (CP), not the Selling Price.

A rational number is a number of the form $\frac{p}{q}$ where $p, q$ are integers and $q \ne 0$.

Examples: $\frac{3}{4}$, $\frac{-2}{5}$, $\frac{7}{1} = 7$, $\frac{0}{3} = 0$.

Standard form: A rational number $\frac{p}{q}$ is in standard form when $q > 0$ and $\text{HCF}(|p|, q) = 1$.

Equivalent rational numbers: Multiply or divide both numerator and denominator by the same non-zero integer.

Comparing rational numbers: Convert to a common positive denominator and compare numerators.

Rational numbers on the number line: Positive rationals lie to the right of $0$, negative rationals to the left.

Between any two rational numbers, there are infinitely many rational numbers.

Memory tip: Every integer is a rational number ($5 = \frac{5}{1}$). Every fraction is a rational number. But not every rational number is a whole number.

Rectangle (length $l$, breadth $b$):

Square (side $a$):

Triangle (base $b$, height $h$):

Parallelogram (base $b$, height $h$):

Circle (radius $r$):

Conversions:
- $1 \text{ cm}^2 = 100 \text{ mm}^2$
- $1 \text{ m}^2 = 10{,}000 \text{ cm}^2$
- $1 \text{ hectare} = 10{,}000 \text{ m}^2$
- $1 \text{ km}^2 = 100 \text{ hectares}$

Memory tip: Area of a parallelogram is the same as a rectangle (base times height), because a parallelogram can be rearranged into a rectangle. A triangle is half a parallelogram.

Definition:

Laws:

Expressing large numbers:

Example: $2^3 \times 2^4 = 2^{3+4} = 2^7 = 128$

Comparing powers: When bases are the same, the number with the larger exponent is greater: $2^5 > 2^3$ because $32 > 8$.

Memory tip: When multiplying same bases, ADD exponents. When dividing same bases, SUBTRACT exponents. When raising a power to a power, MULTIPLY exponents.